Single-Story Frames with Supplementary Bracing

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c.
Single-Story Frames with Supplementary Bracing.
(1) Collapse Mechanism.  The possible collapse mechanisms of
single-story frames with diagonal tension bracing (X-bracing) are presented
in Tables 25 and 26 for pinned-base frames with rigid and non-rigid
girder-to-column connections.  In these tables, the cross-sectional area of
the tension brace is denoted by Ab, the dynamic yield stress for bracing
member is Fdy, and the number of braced bays is denoted by the parameter
m.  In each case, the ultimate capacity of the frame is expressed in terms
of the equivalent static load and the member ultimate strength (either Mp
or AbFdy).  In developing these expressions in the tables, the same
assumptions were made as for rigid frames, i.e., Mp for the roof girder is
constant for all bays, the bay width, L, is constant and the column moment
capacity coefficient, C, is greater than 1.0.  For rigid frames with tension
bracing it is necessary to vary C, C1, and Ab in order to achieve an
economical design.  When non-rigid girder to column connections are used, C
and C1 drop out of the resistance function for the sidesway mechanism and
the area of the bracing can be calculated directly.
(2) Bracing Ductility Ratio.  Tension brace members are not expected
to remain elastic under the blast loading.  Therefore, it is necessary to
determine if this yielding will be excessive when the system is permitted to
deflect to the limits of the design criteria previously given.
(a) The ductility ratio associated with tension yielding of the
bracing is defined as the maximum strain in the brace divided its yield
strain.  Assuming small deflections and neglecting axial deformations in the
girders and columns, the ductility ratio is given by:
EQUATION:
[mu] = [delta] (cos2[gamma])E/LFdy
(117a)
where,
[mu] = ductility ratio
[delta] = sidesway deflection
[gamma] = vertical angle between the bracing and a horizontal plane
L = bay width
(b) From the deflection criteria, the sidesway deflection is
limited to H/50 for reusable structures and to H/25 for non-reusable
structures.  The ductility ratio can be expressed further as:
EQUATION:
[mu] = (H/50L)(cos2[gamma])(E/Fdy)
(117b)
for reusable structures, and as:
EQUATION:
[mu] = (H/25L)(cos2[gamma])(E/Fdy)
(117c)
for non-reusable structures.
2.08-163